We present a new fast active-contour model (a.k.a. snake) for image segmentation in 3D microscopy. We introduce a parametric design that relies on exponential B-spline bases and allows us to build snakes that are able to reproduce ellipsoids. We design our bases to have the shortest-possible support, subject to some constraints. Thus, computational efficiency is maximized. The proposed 3D snake can approximate blob-like objects with good accuracy and can perfectly reproduce spheres and ellipsoids, irrespective of their position and orientation. The optimization process is remarkably fast due to the use of Gauss' theorem within our energy computation scheme. Our technique yields successful segmentation results, even for challenging data where object contours are not well defined. This is due to our parametric approach that allows one to favor prior shapes. In addition, this paper provides a software that gives full control over the snakes via an intuitive manipulation of few control points.